Solutions of systems of differential equations describing general flux problems will be obtained by the finite element method. Such simulation procedures will be combined with an efficient Gauss-Newton non-linear algorithm to provide a general method for determination of least-square estimates of unknown molecular parameters from time-dependent, flow-dependent or steady-state experimental data. Techniques to be studied include ultracentrifugation, molecular exclusion chromatography, electrophorectic methods and isoelectric focusing. The finite element method can be formulated with any of several boundary conditions so as to encompass all types of experimental designs. There are thus no restrictions on the type of experimentally measured data that can be simulated or evaluated (in principle) in terms of molecular parameters by solution of the inverse problem. Since all flux problems are related in principle, a single program can be written in structured form so that reprogramming for new problems can assume trivial proportions. The theory will be applied to several experimental systems that have proven refractory to conventional analysis.